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Volume 5, Issue 1
How Rates of $L^p$-Convergence Carry over to Numerical Approximations of Some Convex, Non-Smooth Functionals of SDEs

Henri Schurz

Int. J. Numer. Anal. Mod., 5 (2008), pp. 55-72.

Published online: 2008-05

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  • Abstract

The relation between weak and $p$-th mean convergence of numerical methods for integration of some convex, non-smooth and path-dependent functionals of ordinary stochastic differential equations (SDEs) is discussed. In particular, we answer how rates of $p$-th mean convergence carry over to rates of weak convergence for such functionals of SDEs in general. Assertions of this type are important for the choice of approximation schemes for discounted price functionals in dynamic asset pricing as met in mathematical finance and other commonly met functionals such as passage times in engineering.

  • Keywords

stochastic differential equations, approximation of convex and path-dependent functionals, numerical methods, stability, $L^p$-convergence, weak convergence, rates of convergence, non-negativity, discounted price functionals, asset pricing, approximation of stochastic exponentials.

  • AMS Subject Headings

65C30, 65L20, 65D30, 34F05, 37H10, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-55, author = {Schurz , Henri}, title = {How Rates of $L^p$-Convergence Carry over to Numerical Approximations of Some Convex, Non-Smooth Functionals of SDEs}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2008}, volume = {5}, number = {1}, pages = {55--72}, abstract = {

The relation between weak and $p$-th mean convergence of numerical methods for integration of some convex, non-smooth and path-dependent functionals of ordinary stochastic differential equations (SDEs) is discussed. In particular, we answer how rates of $p$-th mean convergence carry over to rates of weak convergence for such functionals of SDEs in general. Assertions of this type are important for the choice of approximation schemes for discounted price functionals in dynamic asset pricing as met in mathematical finance and other commonly met functionals such as passage times in engineering.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/797.html} }
TY - JOUR T1 - How Rates of $L^p$-Convergence Carry over to Numerical Approximations of Some Convex, Non-Smooth Functionals of SDEs AU - Schurz , Henri JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 55 EP - 72 PY - 2008 DA - 2008/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/797.html KW - stochastic differential equations, approximation of convex and path-dependent functionals, numerical methods, stability, $L^p$-convergence, weak convergence, rates of convergence, non-negativity, discounted price functionals, asset pricing, approximation of stochastic exponentials. AB -

The relation between weak and $p$-th mean convergence of numerical methods for integration of some convex, non-smooth and path-dependent functionals of ordinary stochastic differential equations (SDEs) is discussed. In particular, we answer how rates of $p$-th mean convergence carry over to rates of weak convergence for such functionals of SDEs in general. Assertions of this type are important for the choice of approximation schemes for discounted price functionals in dynamic asset pricing as met in mathematical finance and other commonly met functionals such as passage times in engineering.

Schurz , Henri. (2008). How Rates of $L^p$-Convergence Carry over to Numerical Approximations of Some Convex, Non-Smooth Functionals of SDEs. International Journal of Numerical Analysis and Modeling. 5 (1). 55-72. doi:
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